Theorem sylc

Description: A syllogism inference combined with contraction. (Contributed by NM, 4-May-1994) (Revised by NM, 13-Jul-2013)

	Ref	Expression
Hypotheses	sylc.1	|- ( ph -> ps )
	sylc.2	|- ( ph -> ch )
	sylc.3	|- ( ps -> ( ch -> th ) )
Assertion	sylc	|- ( ph -> th )

Proof

Step	Hyp	Ref	Expression
1		sylc.1	|- ( ph -> ps )
2		sylc.2	|- ( ph -> ch )
3		sylc.3	|- ( ps -> ( ch -> th ) )
4	1 2 3	syl2im	|- ( ph -> ( ph -> th ) )
5	4	pm2.43i	|- ( ph -> th )